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Conservation of Energy
Conservation of energy states that the total energy of an isolated system remains constant. Energy cannot be created or destroyed The Princess and the Frog In the film The Princess and the Frog, the princess changes from a fully-grown adult into a frog. There is a clear change in mass here, which also means a change in energy as Einstein’s mass-energy equation states, E=mc2, where E is the energy in joules, m is the mass in kilograms and c is the speed of light (approximately 3x108 m/s 1). The average mass of a woman is around 60 kg 2 and so assuming the princess to have this mass also means that the energy associated with her mass would be, E= 60 x (3 x 108)2= 5.4x1018J. The average mass of a wood frog is around 0.01kg to the nearest 10g 3. Assuming the frog that princess turns into to have this mass would mean the associated energy would be, E=0.01 x (3 x 108)2=9.4x1014J. The change in energy is the difference between these values and is found to be around 5.4x1018J. Energy must be conserved which means that this must have been released into the surroundings. This is an enormous amount of energy. The Tsar Bomba was the largest nuclear bomb ever to be detonated and released 50 megatons or 2.01x1017J, under 10% of the estimated energy released in The Princess and the Frog. The Tsar Bomba released enough energy to cause third degree burns a massive 62 miles from the point at which it touched the ground and the shock wave was felt over 500 miles away with it still being strong enough to shatter windows at 560 miles 4. To conclude, it is clear that energy conservation would mean that the conversion of a human to a frog would release an enormous amount of energy. This would have been enough to cause a shock wave that could be felt hundreds if not thousands of miles away, a shock wave which is not illustrated in the film. The Hunger Games: Catching Fire Another example of the conservation of energy is shown by Katniss shooting the force field around the arena in Hunger Games: Catching Fire. She uses a bow to shoot an arrow charged with a bolt of lightning into the force field in order to destroy it. Katniss uses a Hoyt Buffalo Bow 1 which is a recurve bow. Assuming that Katniss shoots the arrow at the top speed of a recurve bow, we can estimate the initial speed of the arrow to be 150mph 2 or around 67 m/s. She appears to shoot the arrow vertically, so we can assume all of the velocity is in the vertical direction. The scene appears to show the arrow travelling for approximately 5 seconds with the acceleration acting in the opposite direction due to gravity. Using SUVAT equations, we can estimate the distance the arrow travels upwards in order to reach the force field. We will neglect air resistance as negligible. S=ut+1/2at2 S= (67)(5) +1/2(-9.81)(5)2 S=212m From this we can calculate the gravitational potential energy, Vgrav, of the arrow as it reaches the force field. We will assume the arrow has a mass of 0.5kg. Vgrav=mgh=(0.5)(9.81)(212)=1040J We can also calculate the velocity, v the arrow will be travelling at this height. v=u+at=67+(-9.81)(5)=18.0 m/s. This gives a kinetic energy of, 1/2mv2=1/2(0.5)(18.0)2=81 By adding the potential and kinetic energy together, we get that the final energy of the arrow is 1121J. Due to the conservation of energy and assuming 100% efficiency, this is the required elastic potential energy, Velastic, in the bow. This energy is stored as Katniss applies a force to the bow, pulling it back before releasing it to shoot the arrow. Assuming that this force is applied over 0.5m, we can find the size of this force. Velastic=FS, Where F is the force that Katniss applies and S is the distance that this force is applied over, 0.5m. 1121=F(0.5) F=2242N This is a massive force, equal to lifting nearly 230kg of mass. The world record for women’s weightlifting is significantly lower at 193kg 3. Katniss would have had to beat this and by using only one arm. 1 http://www.space.com/15830-light-speed.html 2 http://hypertextbook.com/facts/2003/AlexSchlessingerman.shtml 3 http://www.biokids.umich.edu/critters/Lithobates_sylvaticus/ 4 http://www.atomicheritage.org/history/tsar-bomba